We investigate the evaporation of a droplet surrounded by superheated vapor with relative motion between phases. The evaporating droplet is a challenging process, as one must take into account the transport of mass, momentum, and heat. Here a lattice Boltzmann method is employed where phase change is controlled by a nonideal equation of state. First, numerical simulations are compared to the D-2 law for a vaporizing static droplet and good agreement is observed. Results are then presented for a droplet in a Lagrangian frame under a superheated vapor flow. Evaporation is described in terms of the temperature difference between liquid-vapor and the inertial forces. The internal liquid circulation driven by surface-shear stresses due to convection enhances the evaporation rate. Numerical simulations demonstrate that for higher Reynolds numbers, the dynamics of vaporization flux can be significantly affected, which may cause an oscillatory behavior on the droplet evaporation. The droplet-wake interaction and local mass flux are discussed in detail.

We compare dynamic mean-field and dynamic cavity methods to describe the stationary states of dilute kinetic Ising models. We compute dynamic mean-field theory by expanding in interaction strength to third order, and we compare to the exact dynamic mean-field theory for fully asymmetric networks. We show that in diluted networks, the dynamic cavity method generally predicts magnetizations of individual spins better than both first-order ("naive") and second-order ("TAP") dynamic mean-field theory.

We study the problem of optimizing released heat or dissipated work in stochastic thermodynamics. In the overdamped limit these functionals have singular solutions, previously interpreted as protocol jumps. We show that a regularization, penalizing a properly defined acceleration, changes the jumps into boundary layers of finite width. We show that in the limit of vanishing boundary layer width no heat is dissipated in the boundary layer, while work can be done. We further give an alternative interpretation of the fact that the optimal protocols in the overdamped limit are given by optimal deterministic transport (Burgers equation).

We present direct numerical simulations of turbulent channel flow with passive Lagrangian polymers. To understand the polymer behavior we investigate the behavior of infinitesimal line elements and calculate the probability distribution function (PDF) of finite-time Lyapunov exponents and from them the corresponding Cramer's function for the channel flow. We study the statistics of polymer elongation for both the Oldroyd-B model (for Weissenberg number Wi<1) and the FENE model. We use the location of the minima of the Cramer's function to define the Weissenberg number precisely such that we observe coil-stretch transition at Wi1. We find agreement with earlier analytical predictions for PDF of polymer extensions made by Balkovsky, Fouxon, and Lebedev for linear polymers (Oldroyd-B model) with Wi <1 and by Chertkov for nonlinear FENE-P model of polymers. For Wi >1 (FENE model) the polymer are significantly more stretched near the wall than at the center of the channel where the flow is closer to homogenous isotropic turbulence. Furthermore near the wall the polymers show a strong tendency to orient along the streamwise direction of the flow, but near the center line the statistics of orientation of the polymers is consistent with analogous results obtained recently in homogeneous and isotropic flows.

Small particles in suspension in a turbulent fluid have trajectories that do not follow the pathlines of the flow exactly. We investigate the statistics of the angle of deviation φ between the particle and fluid velocities. We show that, when the effects of particle inertia are small, the probability distribution function (PDF) Pφ of this deviation angle shows a power-law region in which Pφ∼φ-4. We also find that the PDFs of the trajectory curvature κ and modulus θ of the torsion have power-law tails that scale, respectively, as Pκ∼κ-5/2, as κ→∞, and Pθ∼θ-3, as θ→∞: These exponents are in agreement with those previously observed for fluid pathlines. We propose a way to measure the complexity of heavy-particle trajectories by the number NI(t,St) of points (up until time t) at which the torsion changes sign. We present numerical evidence that nI(St)≡limt→∞NI(t,St)t∼St-Δ for large St, with Δ≃0.5.

We study spontaneous breakdown of chiral symmetry during the nonlinear evolution of the Tayler instability. We start with an initial steady state of zero helicity. Within linearized perturbation calculations, helical perturbations of this initial state have the same growth rate for either sign of helicity. Direct numerical simulations (DNS) of the fully nonlinear equations, however, show that an infinitesimal excess of one sign of helicity in the initial perturbation gives rise to a saturated helical state. We further show that this symmetry breaking can be described by weakly nonlinear finite-amplitude equations with undetermined coefficients which can be deduced solely from symmetry consideration. By fitting solutions of the amplitude equations to data from DNS, we further determine the coefficients of the amplitude equations.

By means of a simple theoretical model and numerical simulations, we demonstrate the presence of persistent energy currents in a lattice of classical nonlinear oscillators with uniform temperature and chemical potential. In analogy with the well-known Josephson effect, the currents are proportional to the sine of the phase differences between the oscillators. Our results elucidate general aspects of nonequilibrium thermodynamics and point towards a way to practically control transport phenomena in a large class of systems. We apply the model to describe the phase-controlled spin-wave current in a bilayer nanopillar.

We investigate numerically the magnetization dynamics of an array of nanodisks interacting through the magnetodipolar coupling. In the presence of a temperature gradient, the chain reaches a nonequilibrium steady state where energy and magnetization currents propagate. This effect can be described as the flow of energy and particle currents in an off-equilibrium discrete nonlinear Schrodinger (DNLS) equation. This model makes transparent the transport properties of the system and allows for a precise definition of temperature and chemical potential for a precessing spin. The present study proposes a setup for the spin-Seebeck effect, and shows that its qualitative features can be captured by a general oscillator-chain model.

The breakup of small solid aggregates in homogeneous and isotropic turbulence is studied theoretically and by using direct numerical simulations at high Reynolds number, Re-lambda similar or equal to 400. We show that turbulent fluctuations of the hydrodynamic stress along the aggregate trajectory play a key role in determining the aggregate mass distribution function. The differences between turbulent and laminar flows are discussed. A definition of the fragmentation rate is proposed in terms of the typical frequency at which the hydrodynamic stress becomes sufficiently high to cause breakup along each Lagrangian path. We also define an Eulerian proxy of the real fragmentation rate, based on the joint statistics of the stress and its time derivative, which should be easier to measure in any experimental setup. Both our Eulerian and Lagrangian formulations define a clear procedure for the computation of the mass distribution function due to fragmentation. Contrary, previous estimates based only on single point statistics of the hydrodynamic stress exhibit some deficiencies. These are discussed by investigating the evolution of an ensemble of aggregates undergoing breakup and aggregation.

Magnetic field generation on scales that are large compared with the scale of the turbulent eddies is known to be possible via the so-called a effect when the turbulence is helical and if the domain is large enough for the a effect to dominate over turbulent diffusion. Using three-dimensional turbulence simulations, we show that the energy of the resulting mean magnetic field of the saturated state increases linearly with the product of normalized helicity and the ratio of domain scale to eddy scale, provided this product exceeds a critical value of around unity. This implies that large-scale dynamo action commences when the normalized helicity is larger than the inverse scale ratio. Our results show that the emergence of small-scale dynamo action does not have any noticeable effect on the large-scale dynamo. Recent findings by Pietarila Graham et al. [Phys. Rev. E 85, 066406 (2012)] of a smaller minimal helicity may be an artifact due to the onset of small-scale dynamo action at large magnetic Reynolds numbers. However, the onset of large-scale dynamo action is difficult to establish when the kinetic helicity is small. Instead of random forcing, they used an ABC flow with time-dependent phases. We show that such dynamos saturate prematurely in a way that is reminiscent of inhomogeneous dynamos with internal magnetic helicity fluxes. Furthermore, even for very low fractional helicities, such dynamos display large-scale fields that change direction, which is uncharacteristic of turbulent dynamos.

We analyze the angular dynamics of a neutrally buoyant, nearly spherical particle immersed in a steady general linear flow. The hydrodynamic torque acting on the particle is obtained by means of a reciprocal theorem, a regular perturbation theory exploiting the small eccentricity of the nearly spherical particle, and by assuming that inertial effects are small but finite.

We report experiments on the rapid contact-line motion present in the early stages of capillary-driven spreading of drops on dry solid substrates. The spreading data fail to follow a conventional viscous or inertial scaling. By integrating experiments and simulations, we quantify a contact-line friction mu(f) which is seen to limit the speed of the rapid dynamic wetting. A scaling based on this contact-line friction is shown to yield a universal curve for the evolution of the contact-line radius as a function of time, for a range of fluid viscosities, drop sizes, and surface wettabilities.

A method to approximately close the dynamic cavity equations for synchronous reversible dynamics on a locally treelike topology is presented. The method builds on (a) a graph expansion to eliminate loops from the normalizations of each step in the dynamics and (b) an assumption that a set of auxilary probability distributions on histories of pairs of spins mainly have dependencies that are local in time. The closure is then effectuated by projecting these probability distributions on n-step Markov processes. The method is shown in detail on the level of ordinary Markov processes (n = 1) and outlined for higher-order approximations (n > 1). Numerical validations of the technique are provided for the reconstruction of the transient and equilibrium dynamics of the kinetic Ising model on a random graph with arbitrary connectivity symmetry.

In this work we investigate, by means of direct numerical hyperviscous simulations, how rotation affects the bidimensionalization of a turbulent flow. We study a thin layer of fluid, forced by a two-dimensional forcing, within the framework of the "split cascade" in which the injected energy flows both to small scales (generating the direct cascade) and to large scale (to form the inverse cascade). It is shown that rotation reinforces the inverse cascade at the expense of the direct one, thus promoting bidimensionalization of the flow. This is achieved by a suppression of the enstrophy production at large scales. Nonetheless, we find that, in the range of rotation rates investigated, increasing the vertical size of the computational domain causes a reduction of the flux of the inverse cascade. Our results suggest that, even in rotating flows, the inverse cascade may eventually disappear when the vertical scale is sufficiently large with respect to the forcing scale. We also study how the split cascade and confinement influence the breaking of symmetry induced by rotation.

The dynamical behavior of almost neutrally buoyant finite-size rigid fibers or rods in turbulent channel flow is studied by direct numerical simulations. The time evolution of the fiber orientation and translational and rotational motions in a statistically steady channel flow is obtained for three different fiber lengths. The turbulent flow is modeled by an entropy lattice Boltzmann method, and the interaction between fibers and carrier fluid is modeled through an external boundary force method. Direct contact and lubrication force models for fiber-fiber interactions and fiber-wall interaction are taken into account to allow for a full four-way interaction. The density ratio is chosen to mimic cellulose fibers in water. It is shown that the finite size leads to fiber-turbulence interactions that are significantly different from earlier reported results for point like particles (e.g., elongated ellipsoids smaller than the Kolmogorov scale). An effect that becomes increasingly accentuated with fiber length is an accumulation in high-speed regions near the wall, resulting in a mean fiber velocity that is higher than the mean fluid velocity. The simulation results indicate that the finite-size fibers tend to stay in the high-speed streaks due to collisions with the wall. In the central region of the channel, long fibers tend to align in the spanwise direction. Closer to the wall the long fibers instead tend to toward to a rotation in the shear plane, while very close to the wall they become predominantly aligned in the streamwise direction.

Random Boolean networks (RBNs) are used in a number of applications, including cell differentiation, immune response, evolution, gene regulatory networks, and neural networks. This paper addresses the problem of computing attractors in RBNs. An RBN with n vertices has up to 2(n) states. Therefore, for large n, computing attractors by full enumeration of states is not feasible. The state space can be reduced by removing irrelevant vertices, which have no influence on the network's dynamics. In this paper, we show that attractors of an RBN can be computed compositionally from the attractors of the independent components of the subgraph induced by the relevant vertices of the network. The presented approach reduces the complexity of the problem from O(2(n)) to O(2(l)), where l is the number of relevant vertices in the largest component.

For parallel shear flows, transition to turbulence occurs only for perturbations of sufficiently large amplitude. It is therefore relevant to study the shape, amplitude, and dynamics of the least energetic initial disturbances leading to transition. We suggest a numerical approach to find such minimal perturbations, applied here to the case of plane Couette flow. The optimization method seeks such perturbations at initial time as a linear combination of a finite number of linear optimal modes. The energy threshold of the minimal perturbation for a Reynolds number Re=400 is only 2% less than for a pair of symmetric oblique waves. The associated transition scenario shows a long transient approach to a steady state solution with special symmetries. Modal analysis shows how the oblique-wave mechanism can be optimized by the addition of other oblique modes breaking the flow symmetry and whose nonlinear interaction generates spectral components of the edge state. The Re dependence of energy thresholds is revisited, with evidence for a O(Re(-2))-scaling for both oblique waves and streamwise vortices scenarios.

We investigate numerically the dynamics of a laminar-turbulent interface in a spanwisely extended and streamwisely minimal plane Couette flow. The chosen geometry allows one to suppress the large-scale secondary flow and to focus on the nucleation of streaks near the interface. It is shown that the resulting spanwise motion of the interface is essentially stochastic and can be modeled as a continuous-time random walk. This model corresponds here to a Gaussian diffusion process. The average speed of the interface and the corresponding diffusion coefficient are determined as functions of the Reynolds number Re, as well as the threshold value above which turbulence contaminates the whole domain. For the lowest values of Re, the stochastic dynamics competes with another deterministic regime of growth of the localized perturbations. The latter is interpreted as a depinning process from the homoclinic snaking region of the system.

We study inference and reconstruction of couplings in a partially observed kinetic Ising model. With hidden spins, calculating the likelihood of a sequence of observed spin configurations requires performing a trace over the configurations of the hidden ones. This, as we show, can be represented as a path integral. Using this representation, we demonstrate that systematic approximate inference and learning rules can be derived using dynamical mean-field theory. Although naive mean-field theory leads to an unstable learning rule, taking into account Gaussian corrections allows learning the couplings involving hidden nodes. It also improves learning of the couplings between the observed nodes compared to when hidden nodes are ignored.

The nature of the reentrant nematic phase has been actively investigated both experimentally and theoretically during the past few decades. Most studies concluded that, as concerning molecular dynamics, a reentrant nematic phase is essentially analogous to a conventional nematic one. Recent computer simulations [Mazza et al., Phys. Rev. Lett. 105, 227802 (2010)], however, predicted molecular translational self-diffusion along the phase director that was dominated by a collective transport mode and was, relative to that observed in a conventional nematic phase, enhanced by an order of magnitude. In the present work, the principal components of the diffusion tensor in a reentrant nematic phase are determined experimentally and compared to those in conventional nematic and smectic-A phases. We find that the temperature dependence of the translational diffusion in the two nematic phases, within experimental error, follows a uniform trend and can be adequately described in terms of available diffusion models in nematics. Hence, we find no evidence for enhanced diffusion but confirm instead the similarity of conventional and reentrant nematic phases with respect to molecular translational dynamics.

We consider the rotation of small neutrally buoyant axisymmetric particles in a viscous steady shear flow. When inertial effects are negligible the problem exhibits infinitely many periodic solutions, the "Jeffery orbits." We compute how inertial effects lift their degeneracy by perturbatively solving the coupled particle-flow equations. We obtain an equation of motion valid at small shear Reynolds numbers, for spheroidal particles with arbitrary aspect ratios. We analyze how the linear stability of the "log-rolling" orbit depends on particle shape and find it to be unstable for prolate spheroids. This resolves a puzzle in the interpretation of direct numerical simulations of the problem. In general, both unsteady and nonlinear terms in the Navier-Stokes equations are important.

Spatially proximate amino acids in a protein tend to coevolve. A protein's three-dimensional (3D) structure hence leaves an echo of correlations in the evolutionary record. Reverse engineering 3D structures from such correlations is an open problem in structural biology, pursued with increasing vigor as more and more protein sequences continue to fill the data banks. Within this task lies a statistical inference problem, rooted in the following: correlation between two sites in a protein sequence can arise from firsthand interaction but can also be network-propagated via intermediate sites; observed correlation is not enough to guarantee proximity. To separate direct from indirect interactions is an instance of the general problem of inverse statistical mechanics, where the task is to learn model parameters (fields, couplings) from observables (magnetizations, correlations, samples) in large systems. In the context of protein sequences, the approach has been referred to as direct-coupling analysis. Here we show that the pseudolikelihood method, applied to 21-state Potts models describing the statistical properties of families of evolutionarily related proteins, significantly outperforms existing approaches to the direct-coupling analysis, the latter being based on standard mean-field techniques. This improved performance also relies on a modified score for the coupling strength. The results are verified using known crystal structures of specific sequence instances of various protein families. Code implementing the new method can be found at http://plmdca.csc.kth.se/.

Condensation of water vapor on active cloud condensation nuclei produces micron-size water droplets. To form rain, they must grow rapidly into at least 50-to 100-mu m droplets. Observations show that this process takes only 15-20 min. The unexplained physical mechanism of such fast growth is crucial for understanding and modeling of rain and known as "condensation-coalescence bottleneck in rain formation." We show that the recently discovered phenomenon of the tangling clustering instability of small droplets in temperature-stratified turbulence [Phys. Fluids 25, 085104 (2013)] results in the formation of droplet clusters with drastically increased droplet number densities. The mechanism of the tangling clustering instability is much more effective than the previously considered by us the inertial clustering instability caused by the centrifugal effect of turbulent vortices. This is the reason of strong enhancement of the collision-coalescence rate inside the clusters. The mean-field theory of the droplet growth developed in this study can be useful for explanation of the observed fast growth of cloud droplets in warm clouds from the initial 1-mu m-size droplets to 40- to 50-mu m-size dropletswithin 15-20 min.

We study turbulent diffusion of chemically reacting gaseous admixtures in a developed turbulence. In our previous study [Phys. Rev. Lett. 80, 69 (1998)] using a path-integral approach for a delta-correlated in a time random velocity field, we demonstrated a strong modification of turbulent transport in fluid flows with chemical reactions or phase transitions. In the present study we use the spectral tau approximation that is valid for large Reynolds and Peclet numbers and show that turbulent diffusion of the reacting species can be strongly depleted by a large factor that is the ratio of turbulent and chemical times (turbulent Damk "ohler number). We have demonstrated that the derived theoretical dependence of a turbulent diffusion coefficient versus the turbulent Damkohler number is in good agreement with that obtained previously in the numerical modeling of a reactive front propagating in a turbulent flow and described by the Kolmogorov-Petrovskii-Piskunov-Fisher equation. We have found that turbulent cross-effects, e.g., turbulent mutual diffusion of gaseous admixtures and turbulent Dufour effect of the chemically reacting gaseous admixtures, are less sensitive to the values of stoichiometric coefficients. The mechanisms of the turbulent cross-effects differ from the molecular cross-effects known in irreversible thermodynamics. In a fully developed turbulence and at large Peclet numbers the turbulent cross-effects are much larger than the molecular ones. The obtained results are applicable also to heterogeneous phase transitions.

The multidimensional energy surface of a cholesteric liquid crystal in a planar cell is investigated as a function of spherical coordinates determining the director orientation. Minima on the energy surface correspond to the stable states with particular director distribution. External electric and magnetic fields deform the energy surface and positions of minima. It can lead to the transitions between states, known as the Fréedericksz effect. Transitions can be continuous or discontinuous depending on parameters of the liquid crystal which determine an energy surface. In a case of discontinuous transition when a barrier between stable states is comparable with the thermal energy, the activation transitions may occur, and it leads to the modification of characteristics of the Fréedericksz effect with temperature without explicit temperature dependencies of liquid crystal parameters. A minimum energy path between stable states on the energy surface for the Fréedericksz transition is found using the geodesic nudged elastic band method. Knowledge of this path, which has maximal statistical weight among all other paths, gives the information about a barrier between stable states and configuration of director orientation during the transition. It also allows one to estimate the stability of states with respect to the thermal fluctuations and their lifetime when the system is close to the Fréedericksz transition.

We derive explicit, closed-form expressions for the cumulant densities of a multivariate, self-exciting Hawkes point process, generalizing a result of Hawkes in his earlier work on the covariance density and Bartlett spectrum of such processes. To do this, we represent the Hawkes process in terms of a Poisson cluster process and show how the cumulant density formulas can be derived by enumerating all possible "family trees," representing complex interactions between point events. We also consider the problem of computing the integrated cumulants, characterizing the average measure of correlated activity between events of different types, and derive the relevant equations.

Regimes of chemical reaction wave propagating in reactive gaseous mixtures, whose chemistry is governed by chain-branching kinetics, are studied depending on the characteristics of a transient thermal energy deposition localized in a finite volume of reactive gas. Different regimes of the reaction wave propagation are initiated depending on the amount of deposited thermal energy, power of the source, and the size of the hot spot. The main parameters which define regimes of the combustion waves facilitated by the transient deposition of thermal energy are acoustic time scale, duration of the energy deposition, ignition time scale, and size of the hot spot. The interplay between these parameters specifies the role of gasdynamical processes, the formation and steepness of the temperature gradient, and speed of the spontaneous wave. The obtained results show how ignition of one or another combustion regime depends on the value of energy, rate of the energy deposition, and size of the hot spot, which is important for the practical use and for risk assessment.

We present direct numerical simulations of subcritical transition to turbulence in a particle-laden channel flow, with particles assumed rigid, spherical, and heavier than the fluid. The equations describing the fluid flow are solved with an Eulerian mesh, whereas those describing the particle dynamics are solved by Lagrangian tracking. Two-way coupling between fluid and particles is modeled with Stokes drag. The numerical code is first validated against previous results from linear stability: the nonmodal growth of streamwise vortices resulting in streamwise streaks is still the most efficient mechanism for linear disturbance amplification at subcritical conditions as for the case of a single phase fluid. To analyze the full nonlinear transition, we examine two scenarios well studied in the literature: (1) transition initiated by streamwise independent counter-rotating streamwise vortices and one three-dimensional mode and (2) oblique transition, initiated by the nonlinear interaction of two symmetric oblique waves. The threshold energy for transition is computed, and it is demonstrated that for both scenarios the transition may be facilitated by the presence of particles at low number density. This is due to the fact that particles may introduce in the system detrimental disturbances of length scales not initially present. At higher concentrations, conversely, we note an increase of the disturbance energy needed for transition. The threshold energy for the oblique scenario shows a more significant increase in the presence of particles, by a factor about four. Interestingly, for the streamwise-vortex scenario the time at which transition occurs increases with the particle volume fraction when considering disturbances of equal initial energy. These results are explained by considering the reduced amplification of oblique modes in the two-phase flow. The results from these two classical scenarios indicate that, although linear stability analysis shows hardly any effect on optimal growth, particles do influence secondary instabilities and streak breakdown. These effects can be responsible of the reduced drag observed in turbulent channel flow laden with heavy particles.

The equations of motion of a single particle subject to an arbitrary electric and a static magnetic field form a Poisson system. We present a second-order time integration method which preserves well the Poisson structure and compare it to commonly used algorithms, such as the Boris scheme. All the methods are represented in a general framework of splitting methods. We use the so-called phi functions, which give efficient ways for both analyzing and implementing the algorithms. Numerical experiments show an excellent long term stability for the method considered.

We present a modeling approach that enables numerical simulations of a boiling Van der Waals fluid based on the diffuse interface description. A boundary condition is implemented that allows in and out flux of mass at constant external pressure. In addition, a boundary condition for controlled wetting properties of the boiling surface is also proposed. We present isothermal verification cases for each element of our modeling approach. By using these two boundary conditions we are able to numerically access a system that contains the essential physics of the boiling process at microscopic scales. Evolution of bubbles under film boiling and nucleate boiling conditions are observed by varying boiling surface wettability. We observe flow patters around the three-phase contact line where the phase change is greatest. For a hydrophilic boiling surface, a complex flow pattern consistent with vapor recoil theory is observed.

We introduce variable focused local search algorithms for satisfiabiliity problems. Usual approaches focus uniformly on unsatisfied clauses. The methods described here work by focusing on random variables in unsatisfied clauses. Variants are considered where variables are selected uniformly and randomly or by introducing a bias towards picking variables participating in several unsatistified clauses. These are studied in the case of the random 3-SAT problem, together with an alternative energy definition, the number of variables in unsatisfied constraints. The variable-based focused Metropolis search (V-FMS) is found to be quite close in performance to the standard clause-based FMS at optimal noise. At infinite noise, instead, the threshold for the linearity of solution times with instance size is improved by picking preferably variables in several UNSAT clauses. Consequences for algorithmic design are discussed.

Many modern nanostructured materials and doped polymers are morphologically too complex to be interpreted by classical percolation theory. Here, we develop the concept of a hierarchical percolating (percolation-within-percolation) system to describe such complex materials and illustrate how to generalize the conventional percolation to double-level percolation. Based on Monte Carlo simulations, we find that the double-level percolation threshold is close to, but definitely larger than, the product of the local percolation thresholds for the two enclosed single-level systems. The deviation may offer alternative insights into physics concerning infinite clusters and open up new research directions for percolation theory.

This Rapid Communication proposes a comprehensive scaling theory for percolation, which clarifies the intrinsic nature of finite-size scaling and effectively addresses the finite-size effects. This theory applies to extensive systems, including especially the explosive percolation. It is suggested that explosive percolation shares the same scaling law as normal percolation, but may suffer from more severe finite-size effects. Remarkably, in contrast to previous studies, relying on the framework of our theory, the present Rapid Communication suggests that for all systems, the universal scaling functions do not depend on the boundary conditions.

The present paper introduces an efficient Monte Carlo algorithm for continuum percolation composed of randomly oriented rectangles. By conducting extensive simulations, we report high-precision percolation thresholds for a variety of homogeneous systems with different rectangle aspect ratios. This paper verifies and extends the excluded area theory. It is confirmed that percolation thresholds are dominated by the average excluded areas for both homogeneous and heterogeneous rectangle systems (except for some special heterogeneous systems where the rectangle lengths differ too much from one another). In terms of the excluded areas, generalized formulas are proposed to effectively predict precise percolation thresholds for all these rectangle systems. This paper is, therefore, helpful for both practical applications and theoretical studies concerning relevant systems.

We propose a method for efficient simulations in extended ensembles, useful, e. g., for the study of problems with complex energy landscapes and for free energy calculations. The main difficulty in such simulations is the estimation of the a priori unknown weight parameters needed to produce flat histograms. The method combines several complementary techniques, namely, a Gibbs sampler for the parameter moves, a reweighting procedure to optimize data use, and a Bayesian update allowing for systematic refinement of the free energy estimate. In a certain limit the scheme reduces to the 1/t algorithm of B. E. Belardinelli and V. D. Pereyra [Phys. Rev. E 75, 046701 (2007)]. The performance of the method is studied on the two-dimensional Ising model, where comparison with the exact free energy is possible, and on an Ising spin glass.

The effect of the inhomogeneous environment upon solvent molecules close to a macromolecular surface is evaluated from a molecular-dynamics simulation of a protein, myoglobin, in water solution. The simulation is analyzed in terms of a mean-field potential from the protein upon the water molecules and spatially varying translational diffusion coefficients for solvent molecules in directions parallel and perpendicular to the protein surface. The diffusion coefficients can be obtained from the slope of the average-square displacements vs time, as well as from the integral of the velocity autocorrelation functions. It is shown that the former procedure gives a lot of ambiguities due to the variation of the slope of the curve with time. The latter, however, after analytic correction for the contribution from algebraic long-time tails, furnish a much more reliable alternative.

We study the geometry of biopolymer networks and effects of the geometry on bulk mechanical properties. It is shown numerically that the physical network geometry can be quantified statistically and regenerated from its statistical description, so that the regenerated network exhibits the same network mechanics as the physical network in the elastic regime. A collagen-I biopolymer network is used for validation. The method enables parametric studies of the network geometry, whose parameters are often difficult to vary independently in experiments.

Multicomponent, multiphase, compressible flows are very important in real life, as well as in scientific research, while their modeling is in an early stage. In this paper, we propose a diffuse interface model for compressible binary mixtures, based on the balance of mass, momentum, energy, and the second law of thermodynamics. We show both analytically and numerically that this model is able to describe the phase equilibrium for a real binary mixture (CO2 + ethanol is considered in this paper) very well by adjusting the parameter which measures the attraction force between molecules of the two components in the model. We also show that the calculated surface tension of the CO2 + ethanol mixture at different concentrations match measurements in the literature when the mixing capillary coefficient is taken to be the geometric mean of the capillary coefficient of each component. Three different cases of two droplets in a shear flow, with the same or different concentration, are simulated, showing that the higher concentration of CO2 the smaller the surface tension and the easier the drop deforms.

We numerically study the thermohydrodynamics of boiling for a CO2 + ethanol mixture on lyophilic and lyophobic surfaces in both closed and open systems, based on a diffuse interface model for a two-component system. The corresponding wetting boundary conditions for an isothermal system are proposed and verified in this paper. New phenomena due to the addition of another component, mainly the preferential evaporation of the more volatile component, are observed. In the open system and the closed system, the physical process shows very different characteristics. In the open system, except for the movement of the contact line, the qualitative features are rather similar for lyophobic and lyophilic surfaces. In the closed system, the vortices that are observed on a lyophobic surface are not seen on a lyophilic surface. More sophisticated wetting boundary conditions for nonisothermal, two-component systems might need to be further developed, taking into account the variations of density, temperature, and surface tension near the wall, while numerical results show that the boundary conditions proposed here also work well even in boiling, where the temperature is nonuniform.

The dynamics of a kicked quantum mechanical wave packet at a quantum resonance is studied in the framework of Floquet analysis. It is seen how a directed current can be created out of a homogeneous initial state at certain resonances in an asymmetric potential. The almost periodic parameter dependence of the current is found to be connected with level crossings in the Floquet spectrum.

The Fortuin-Kasteleyn and heat-bath damage-spreading temperatures T FK(p) and T DS(p) are studied on random-bond Ising models of dimensions 2-5 and as functions of the ferromagnetic interaction probability p; the conjecture that T DS(p)∼T FK(p) is tested. It follows from a statement by Nishimori that in any such system, exact coordinates can be given for the intersection point between the Fortuin-Kasteleyn T FK(p) transition line and the Nishimori line [p NL,FK, T NL,FK]. There are no finite-size corrections for this intersection point. In dimension 3, at the intersection concentration [p NL,FK], the damage spreading T DS(p) is found to be equal to T FK(p) to within 0.1%. For the other dimensions, however, T DS(p) is observed to be systematically a few percent lower than T FK(p).

In the simple [hyper]cubic five-dimension, near-neighbor-interaction Ising ferromagnet, extensive simulation measurements are made of the link overlap and the spin overlap distributions. These "two replica" measurements are standard in the spin glass context but are not usually recorded in ferromagnet simulations. The moments and moment ratios of these distributions (the variance, the kurtosis, and the skewness) show clear critical behaviors at the known ordering temperature of the ferromagnet. Analogous overlap effects can be expected quite generally in Ising ferromagnets in any dimension. The link overlap results in particular, with peaks at criticality in the kurtosis and the skewness, also have implications for spin glasses.

We report the observation of a doubly periodic surface defect pattern in the liquid crystal 8CB, formed during the nematic-smectic-A phase transition. The pattern results from the antagonistic alignment of the 8CB molecules, which is homeotropic at the surface and planar in the bulk of the sample cell. Within the continuum Landau-de Gennes theory of smectic liquid crystals, we find that the long period (approximate to 10 mu m) of the pattern is given by the balance between the surface anchoring and the elastic energy of curvature wall defects. The short period (approximate to 10 mu m) we attribute to a saddle-splay distortion, leading to a nonzero Gaussian curvature and causing the curvature walls to break up.

Collective behavior of proteins on biomembranes is usually studied within the spontaneous curvature model. Here we consider an alternative phenomenological approach, which accounts consistently for partial ordering of proteins as well as the anchoring forces exerted on a membrane by layer of proteins. We show analytically that such anisotropic interactions can drive membrane bending, resulting in nontrivial equilibrium morphologies. The predicted instabilities can advance our conceptual understanding of physical mechanisms behind collective phenomena in biological systems, in particular those with inherent anisotropy.

We analyze the translational and rotational motion of an ellipsoidal Brownian particle from the viewpoint of stochastic thermodynamics. The particle's Brownian motion is driven by external forces and torques and takes place in an heterogeneous thermal environment where friction coefficients and (local) temperature depend on space and time. Our analysis of the particle's stochastic thermodynamics is based on the entropy production associated with single particle trajectories. It is motivated by the recent discovery that the overdamped limit of vanishing inertia effects (as compared to viscous fricion) produces a so-called "anomalous" contribution to the entropy production, which has no counterpart in the overdamped approximation, when inertia effects are simply discarded. Here we show that rotational Brownian motion in the overdamped limit generates an additional contribution to the "anomalous" entropy. We calculate its specific form by performing a systematic singular perturbation analysis for the generating function of the entropy production. As a side result, we also obtain the (well-known) equations of motion in the overdamped limit. We furthermore investigate the effects of particle shape and give explicit expressions of the "anomalous entropy" for prolate and oblate spheroids and for near-spherical Brownian particles.

The vast majority of parallel scientific applications distributes computation among processes that are in a busy state when computing and in an idle state when waiting for information from other processes. We identify the propagation of idle waves through processes in scientific applications with a local information exchange between the two processes. Idle waves are nondispersive and have a phase velocity inversely proportional to the average busy time. The physical mechanism enabling the propagation of idle waves is the local synchronization between two processes due to remote data dependency. This study provides a description of the large number of processes in parallel scientific applications as a continuous medium. This work also is a step towards an understanding of how localized idle periods can affect remote processes, leading to the degradation of global performance in parallel scientific applications.

We report a molecular dynamics simulation demonstrating that the smectic-B crystalline phase (Cry-B), commonly observed in mesogenic systems of anisotropic molecules, can be formed by a system of identical particles interacting via a spherically symmetric potential. The Cry-B phase forms as a result of a first-order transition from an isotropic liquid phase upon isochoric cooling at appropriate number density. Its structure, determined by the design of the pair potential, corresponds to the Cry-B structure formed by elongated particles with the aspect ratio 1.8. The diffraction pattern and the real-space structure inspection demonstrate dominance of the ABC-type of axial layer stacking. This result opens a general possibility of producing smectic phases using isotropic interparticle interaction both in simulations and in colloidal systems.

We solve for the motion of charged particles in a helical time-periodic ABC (Arnold-Beltrami-Childress) magnetic field. The magnetic field lines of a stationary ABC field with coefficients A=B=C=1 are chaotic, and we show that the motion of a charged particle in such a field is also chaotic at late times with positive Lyapunov exponent. We further show that in time-periodic ABC fields, the kinetic energy of a charged particle can increase indefinitely with time. At late times the mean kinetic energy grows as a power law in time with an exponent that approaches unity. For an initial distribution of particles, whose kinetic energy is uniformly distributed within some interval, the probability density function of kinetic energy is, at late times, close to a Gaussian but with steeper tails.

Although the capillary spreading of a drop on a dry substrate is well studied, understanding and describing the physical mechanisms that govern the dynamics remain challenging. Here we study the dynamics of spreading of partially wetting nanodroplets by combining molecular dynamics simulations and continuum phase field simulations. The phase field simulations account for all the relevant hydrodynamics, i.e., capillarity, inertia, and viscous stresses. By coordinated continuum and molecular dynamics simulations, the macroscopic model parameters are extracted. For a Lennard-Jones fluid spreading on a planar surface, the liquid slip at the solid substrate is found to be significant, in fact crucial for the motion of the contact line. Evaluation of the different contributions to the energy transfer shows that the liquid slip generates dissipation of the same order as the bulk viscous dissipation or the energy transfer to kinetic energy. We also study the dynamics of spreading on a substrate with a periodic nanostructure. Here it is found that a nanostructure with a length scale commensurate with molecular size completely inhibits the liquid slip. The dynamic spreading is thus about 30% slower on a nanostructured surface compared to one that is atomically smooth.

The low-energy physics of (quasi) degenerate one-dimensional systems is typically understood as the particlelike dynamics of kinks between stable, ordered structures. Such dynamics, we show, becomes highly nontrivial when the ground states are topologically constrained: a dynamics of the domains rather than on the domains which the kinks separate. Motivated by recently reported observations of charged polymers physio-adsorbed on nanotubes, we study kinks between helical structures of a string wrapping around a cylinder. While their motion cannot be disentangled from domain dynamics, and energy and momentum is not concentrated in the solitons, the dynamics of the domains can be folded back into a particle-like description of the local excitations.